equilibrium kinetic energy should be *half* of what you initially assign

Dear Lammps users,

In the webpage
http://sourceforge.net/p/lammps/mailman/message/31607022/

it is mentioned that:
the only way to confirm this,is to run *without* a thermostat.
energy has to be conserved by that,and if you start of an optimal
structure the equilibrium kinetic energy should be *half* of what
you initially assign.
and that:
try running with fix nve and without *any* thermostat, just the
initial temperature assignment.if your system is properly relaxed
and minimized the final temperature should be about half the initial
value.

I need some explanation.

Thanks for the help,
Erchia

Dear Lammps users,

In the webpage
http://sourceforge.net/p/lammps/mailman/message/31607022/

it is mentioned that:
the only way to confirm this,is to run without a thermostat.
energy has to be conserved by that,and if you start of an optimal
structure the equilibrium kinetic energy should be half of what
you initially assign.
and that:
try running with fix nve and without any thermostat, just the
initial temperature assignment.if your system is properly relaxed
and minimized the final temperature should be about half the initial
value.

I need some explanation.

Please pick up a decent textbook about MD and read about equilibration and how kinetic energy is converted into potential energy in the process (or vice versa).

Axel